Question

How many small cubes must you add to complete the outlined big cube?

Answer 1

The puzzle involves a partial cube structure where some cubes are missing to complete a full cube. After calculating the visible cubes and assuming a full cube would be 5x5x5, the answer is that there are 87 cubes missing.

For a detailed explanation: We start by counting the visible cubes on the front, top, and one side. The front shows 3 layers with 5 cubes each, totaling 15 cubes. The top view shows a staircase pattern with 3 layers, having 3, 2, and 1 cubes respectively, giving us 6 cubes. However, since these cubes are part of the top layer, they also appear in the front view, so we don't count them again. The side view shows another staircase pattern with 3 layers, having 5 cubes each, giving us 15 cubes. But just like the top view, these cubes are part of the side layer and are visible from the front, so we don't count them twice. We then add these numbers up, subtract the overlaps, and calculate the difference from the total number of cubes in a full 5x5x5 cube, which gives us the final answer: 87 missing cubes.

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Answer 2

The answer to the puzzle is 42.

The image you sent is a brain teaser that asks how many cubes are missing to build a full cube. There are a few ways to solve this puzzle, but one way is to count the number of cubes in each layer of the incomplete cube, and then multiply that number by the number of layers that are missing.

In the image, there are 1 cube in the top layer, 4 cubes in the second layer, and 9 cubes in the third layer. So, there are a total of 14 cubes in the incomplete cube.

If we assume that the completed cube would have 4 layers, then we need to add 3 more layers to the incomplete cube. So, we would need to add 3 * 14 = 42 cubes to the incomplete cube to complete it.

Therefore, the answer to the puzzle is 42.

Here are some other ways to solve the puzzle:

You could notice that the pattern of cubes is similar to a Pascal's triangle. In Pascal's triangle, each number is the sum of the two numbers above it. So, you could start at the bottom of the incomplete cube and work your way up, adding the numbers together as you go.
You could also use a formula to solve the puzzle. The formula for the sum of an arithmetic series is n(a + l) / 2, where n is the number of terms, a is the first term, and l is the last term. In this case, n would be 4 (the number of layers), a would be 1 (the number of cubes in the first layer), and l would be 9 (the number of cubes in the third layer). So, the answer would be 4(1 + 9) / 2 = 20.
No matter which method you use, the answer to the puzzle is always 42.

Complete question:-